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We develop a theory in order to describe the effect of relaxation in acondensed medium upon the quantum decay of a metastable liquid near thespinodal at low temperatures. We find that both the regime and the rate ofquantum nucleation strongly depend on the relaxation time and its temperaturebehavior. The quantum nucleation rate slows down with the decrease of therelaxation time. We also discuss the low temperature experiments on cavitationin normal $^3$He and superfluid $^4$He at negative pressures. It is the sharpdistinctions in the high frequency sound mode and in the temperature behaviorof the relaxation time that make the quantum cavitation kinetics in $^3$He and$^4$He completely different in kind.Comment: 10 pages, 2 figure

Underbarrier nucleation kinetics in a metastable quantum liquid near the liquid-gas spinodal line